LMFDB - Embedded newform 135.4.e.b.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,4,Mod(46,135)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("135.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	135.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.96525785077$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.15759792.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 $ x^6 - 3x^5 + 16x^4 - 27x^3 + 52x^2 - 39*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			91.2
Root			$0.500000 + 1.98116i$ of defining polynomial
Character	$\chi$	$=$	135.91
Dual form			135.4.e.b.46.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0874923 - 0.151541i) q^{2} +(3.98469 - 6.90169i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-4.23186 - 7.32979i) q^{7} -2.79440 q^{8} +O(q^{10})$	\(q+(-0.0874923 - 0.151541i) q^{2} +(3.98469 - 6.90169i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-4.23186 - 7.32979i) q^{7} -2.79440 q^{8} -0.874923 q^{10} +(-15.7541 - 27.2870i) q^{11} +(-13.4348 + 23.2697i) q^{13} +(-0.740510 + 1.28260i) q^{14} +(-31.6330 - 54.7900i) q^{16} +44.3307 q^{17} -90.2082 q^{19} +(-19.9235 - 34.5084i) q^{20} +(-2.75673 + 4.77480i) q^{22} +(97.1287 - 168.232i) q^{23} +(-12.5000 - 21.6506i) q^{25} +4.70176 q^{26} -67.4506 q^{28} +(1.87186 + 3.24215i) q^{29} +(125.832 - 217.947i) q^{31} +(-16.7129 + 28.9476i) q^{32} +(-3.87859 - 6.71792i) q^{34} -42.3186 q^{35} -62.2293 q^{37} +(7.89252 + 13.6703i) q^{38} +(-6.98599 + 12.1001i) q^{40} +(-102.173 + 176.969i) q^{41} +(263.831 + 456.968i) q^{43} -251.101 q^{44} -33.9920 q^{46} +(77.8637 + 134.864i) q^{47} +(135.683 - 235.009i) q^{49} +(-2.18731 + 3.78853i) q^{50} +(107.067 + 185.445i) q^{52} +141.694 q^{53} -157.541 q^{55} +(11.8255 + 20.4823i) q^{56} +(0.327546 - 0.567326i) q^{58} +(-246.923 + 427.683i) q^{59} +(379.742 + 657.732i) q^{61} -44.0373 q^{62} -500.280 q^{64} +(67.1739 + 116.349i) q^{65} +(271.795 - 470.763i) q^{67} +(176.644 - 305.956i) q^{68} +(3.70255 + 6.41300i) q^{70} +928.207 q^{71} +608.739 q^{73} +(5.44459 + 9.43030i) q^{74} +(-359.452 + 622.589i) q^{76} +(-133.338 + 230.949i) q^{77} +(-307.420 - 532.467i) q^{79} -316.330 q^{80} +35.7573 q^{82} +(537.655 + 931.246i) q^{83} +(110.827 - 191.957i) q^{85} +(46.1663 - 79.9623i) q^{86} +(44.0233 + 76.2506i) q^{88} -1505.15 q^{89} +227.416 q^{91} +(-774.055 - 1340.70i) q^{92} +(13.6249 - 23.5991i) q^{94} +(-225.521 + 390.613i) q^{95} +(166.369 + 288.160i) q^{97} -47.4848 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8}+O(q^{10}) $ 6 * q - q^2 - 11 * q^4 + 15 * q^5 + 43 * q^7 + 54 * q^8	$ 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8} - 10 q^{10} + 14 q^{11} - 40 q^{13} - 27 q^{14} + 13 q^{16} + 332 q^{17} - 328 q^{19} + 55 q^{20} + 376 q^{22} + 171 q^{23} - 75 q^{25} - 868 q^{26} - 1034 q^{28} - 335 q^{29} + 352 q^{31} - 77 q^{32} + 52 q^{34} + 430 q^{35} + 804 q^{37} - 178 q^{38} + 135 q^{40} + 187 q^{41} + 602 q^{43} - 1964 q^{44} - 402 q^{46} + 665 q^{47} - 430 q^{49} - 25 q^{50} + 456 q^{52} + 1460 q^{53} + 140 q^{55} + 705 q^{56} - 217 q^{58} - 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 3138 q^{64} + 200 q^{65} + 1849 q^{67} - 710 q^{68} + 135 q^{70} - 140 q^{71} - 736 q^{73} - 320 q^{74} - 204 q^{76} - 948 q^{77} + 382 q^{79} + 130 q^{80} - 1150 q^{82} - 831 q^{83} + 830 q^{85} + 1580 q^{86} + 1428 q^{88} - 3438 q^{89} - 1420 q^{91} - 1623 q^{92} + 2077 q^{94} - 820 q^{95} + 282 q^{97} - 4328 q^{98}+O(q^{100}) $ 6 * q - q^2 - 11 * q^4 + 15 * q^5 + 43 * q^7 + 54 * q^8 - 10 * q^10 + 14 * q^11 - 40 * q^13 - 27 * q^14 + 13 * q^16 + 332 * q^17 - 328 * q^19 + 55 * q^20 + 376 * q^22 + 171 * q^23 - 75 * q^25 - 868 * q^26 - 1034 * q^28 - 335 * q^29 + 352 * q^31 - 77 * q^32 + 52 * q^34 + 430 * q^35 + 804 * q^37 - 178 * q^38 + 135 * q^40 + 187 * q^41 + 602 * q^43 - 1964 * q^44 - 402 * q^46 + 665 * q^47 - 430 * q^49 - 25 * q^50 + 456 * q^52 + 1460 * q^53 + 140 * q^55 + 705 * q^56 - 217 * q^58 - 298 * q^59 + 1439 * q^61 + 3228 * q^62 - 3138 * q^64 + 200 * q^65 + 1849 * q^67 - 710 * q^68 + 135 * q^70 - 140 * q^71 - 736 * q^73 - 320 * q^74 - 204 * q^76 - 948 * q^77 + 382 * q^79 + 130 * q^80 - 1150 * q^82 - 831 * q^83 + 830 * q^85 + 1580 * q^86 + 1428 * q^88 - 3438 * q^89 - 1420 * q^91 - 1623 * q^92 + 2077 * q^94 - 820 * q^95 + 282 * q^97 - 4328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0874923	−	0.151541i	−0.0309332	−	0.0535779i	0.850144	−	0.526550i	$-0.176515\pi$
$2$	−0.0874923	−	0.151541i	−0.0309332	−	0.0535779i	−0.881078	+	0.472972i	$0.843181\pi$
$3$		0			0
$3$		0			0
$4$	3.98469	−	6.90169i	0.498086	−	0.862711i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	−4.23186	−	7.32979i	−0.228499	−	0.395772i	0.728865	−	0.684658i	$-0.240048\pi$
$7$	−4.23186	−	7.32979i	−0.228499	−	0.395772i	−0.957363	+	0.288886i	$0.906715\pi$
$8$	−2.79440			−0.123496
$9$		0			0
$10$	−0.874923			−0.0276675
$11$	−15.7541	−	27.2870i	−0.431823	−	0.747939i	0.565208	−	0.824949i	$-0.308796\pi$
$11$	−15.7541	−	27.2870i	−0.431823	−	0.747939i	−0.997030	+	0.0770098i	$0.975463\pi$
$12$		0			0
$13$	−13.4348	+	23.2697i	−0.286626	+	0.496451i	−0.973002	−	0.230796i	$-0.925867\pi$
$13$	−13.4348	+	23.2697i	−0.286626	+	0.496451i	0.686376	+	0.727247i	$0.259200\pi$
$14$	−0.740510	+	1.28260i	−0.0141364	+	0.0244850i
$15$		0			0
$16$	−31.6330	−	54.7900i	−0.494266	−	0.856094i
$17$	44.3307			0.632457			0.316229	−	0.948683i	$-0.397583\pi$
$17$	44.3307			0.632457			0.316229	+	0.948683i	$0.397583\pi$
$18$		0			0
$19$	−90.2082			−1.08922			−0.544610	−	0.838689i	$-0.683322\pi$
$19$	−90.2082			−1.08922			−0.544610	+	0.838689i	$0.683322\pi$
$20$	−19.9235	−	34.5084i	−0.222751	−	0.385816i
$21$		0			0
$22$	−2.75673	+	4.77480i	−0.0267153	+	0.0462723i
$23$	97.1287	−	168.232i	0.880553	−	1.52516i	0.0298265	−	0.999555i	$-0.490505\pi$
$23$	97.1287	−	168.232i	0.880553	−	1.52516i	0.850727	−	0.525608i	$-0.176162\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	4.70176			0.0354650
$27$		0			0
$28$	−67.4506			−0.455248
$29$	1.87186	+	3.24215i	0.0119860	+	0.0207604i	0.871956	−	0.489584i	$-0.162851\pi$
$29$	1.87186	+	3.24215i	0.0119860	+	0.0207604i	−0.859970	+	0.510344i	$0.829518\pi$
$30$		0			0
$31$	125.832	−	217.947i	0.729035	−	1.26273i	−0.228257	−	0.973601i	$-0.573303\pi$
$31$	125.832	−	217.947i	0.729035	−	1.26273i	0.957292	−	0.289124i	$-0.0933641\pi$
$32$	−16.7129	+	28.9476i	−0.0923265	+	0.159914i
$33$		0			0
$34$	−3.87859	−	6.71792i	−0.0195639	−	0.0338857i
$35$	−42.3186			−0.204376
$36$		0			0
$37$	−62.2293			−0.276498			−0.138249	−	0.990397i	$-0.544147\pi$
$37$	−62.2293			−0.276498			−0.138249	+	0.990397i	$0.544147\pi$
$38$	7.89252	+	13.6703i	0.0336931	+	0.0583581i
$39$		0			0
$40$	−6.98599	+	12.1001i	−0.0276145	+	0.0478298i
$41$	−102.173	+	176.969i	−0.389188	+	0.674094i	−0.992341	−	0.123532i	$-0.960578\pi$
$41$	−102.173	+	176.969i	−0.389188	+	0.674094i	0.603152	+	0.797626i	$0.293911\pi$
$42$		0			0
$43$	263.831	+	456.968i	0.935669	+	1.62063i	0.773436	+	0.633874i	$0.218536\pi$
$43$	263.831	+	456.968i	0.935669	+	1.62063i	0.162233	+	0.986752i	$0.448130\pi$
$44$	−251.101			−0.860340
$45$		0			0
$46$	−33.9920			−0.108953
$47$	77.8637	+	134.864i	0.241651	+	0.418551i	0.961185	−	0.275906i	$-0.0889778\pi$
$47$	77.8637	+	134.864i	0.241651	+	0.418551i	−0.719534	+	0.694457i	$0.755645\pi$
$48$		0			0
$49$	135.683	−	235.009i	0.395577	−	0.685159i
$50$	−2.18731	+	3.78853i	−0.00618664	+	0.0107156i
$51$		0			0
$52$	107.067	+	185.445i	0.285529	+	0.494551i
$53$	141.694			0.367230			0.183615	−	0.982998i	$-0.441220\pi$
$53$	141.694			0.367230			0.183615	+	0.982998i	$0.441220\pi$
$54$		0			0
$55$	−157.541			−0.386234
$56$	11.8255	+	20.4823i	0.0282187	+	0.0488762i
$57$		0			0
$58$	0.327546	−	0.567326i	0.000741533	−	0.00128437i
$59$	−246.923	+	427.683i	−0.544857	+	0.943721i	0.453758	+	0.891125i	$0.350083\pi$
$59$	−246.923	+	427.683i	−0.544857	+	0.943721i	−0.998616	+	0.0525961i	$0.983250\pi$
$60$		0			0
$61$	379.742	+	657.732i	0.797065	+	1.38056i	0.921520	+	0.388331i	$0.126948\pi$
$61$	379.742	+	657.732i	0.797065	+	1.38056i	−0.124455	+	0.992225i	$0.539718\pi$
$62$	−44.0373			−0.0902055
$63$		0			0
$64$	−500.280			−0.977108
$65$	67.1739	+	116.349i	0.128183	+	0.222020i
$66$		0			0
$67$	271.795	−	470.763i	0.495598	−	0.858401i	−0.504389	−	0.863476i	$-0.668282\pi$
$67$	271.795	−	470.763i	0.495598	−	0.858401i	0.999987	+	0.00507574i	$0.00161566\pi$
$68$	176.644	−	305.956i	0.315018	−	0.545627i
$69$		0			0
$70$	3.70255	+	6.41300i	0.00632199	+	0.0109500i
$71$	928.207			1.55152			0.775760	−	0.631028i	$-0.217367\pi$
$71$	928.207			1.55152			0.775760	+	0.631028i	$0.217367\pi$
$72$		0			0
$73$	608.739			0.975993			0.487997	−	0.872845i	$-0.337728\pi$
$73$	608.739			0.975993			0.487997	+	0.872845i	$0.337728\pi$
$74$	5.44459	+	9.43030i	0.00855298	+	0.0148142i
$75$		0			0
$76$	−359.452	+	622.589i	−0.542526	+	0.939682i
$77$	−133.338	+	230.949i	−0.197342	+	0.341806i
$78$		0			0
$79$	−307.420	−	532.467i	−0.437816	−	0.758319i	0.559705	−	0.828692i	$-0.310915\pi$
$79$	−307.420	−	532.467i	−0.437816	−	0.758319i	−0.997521	+	0.0703726i	$0.977581\pi$
$80$	−316.330			−0.442085
$81$		0			0
$82$	35.7573			0.0481553
$83$	537.655	+	931.246i	0.711028	+	1.23154i	0.964472	+	0.264186i	$0.0851033\pi$
$83$	537.655	+	931.246i	0.711028	+	1.23154i	−0.253444	+	0.967350i	$0.581563\pi$
$84$		0			0
$85$	110.827	−	191.957i	0.141422	−	0.244950i
$86$	46.1663	−	79.9623i	0.0578865	−	0.100262i
$87$		0			0
$88$	44.0233	+	76.2506i	0.0533284	+	0.0923675i
$89$	−1505.15			−1.79265			−0.896324	−	0.443400i	$-0.853772\pi$
$89$	−1505.15			−1.79265			−0.896324	+	0.443400i	$0.853772\pi$
$90$		0			0
$91$	227.416			0.261975
$92$	−774.055	−	1340.70i	−0.877183	−	1.51933i
$93$		0			0
$94$	13.6249	−	23.5991i	0.0149501	−	0.0258943i
$95$	−225.521	+	390.613i	−0.243557	+	0.421853i
$96$		0			0
$97$	166.369	+	288.160i	0.174147	+	0.301631i	0.939866	−	0.341544i	$-0.110950\pi$
$97$	166.369	+	288.160i	0.174147	+	0.301631i	−0.765719	+	0.643175i	$0.777617\pi$
$98$	−47.4848			−0.0489458
$99$		0			0
$100$	−199.235			−0.199235
$101$	−247.493	−	428.670i	−0.243826	−	0.422319i	0.717975	−	0.696069i	$-0.245069\pi$
$101$	−247.493	−	428.670i	−0.243826	−	0.422319i	−0.961801	+	0.273750i	$0.911736\pi$
$102$		0			0
$103$	315.015	−	545.622i	0.301353	−	0.521959i	−0.675090	−	0.737736i	$-0.735895\pi$
$103$	315.015	−	545.622i	0.301353	−	0.521959i	0.976443	+	0.215777i	$0.0692284\pi$
$104$	37.5421	−	65.0248i	0.0353972	−	0.0613097i
$105$		0			0
$106$	−12.3971	−	21.4725i	−0.0113596	−	0.0196754i
$107$	1561.00			1.41035			0.705175	−	0.709034i	$-0.250869\pi$
$107$	1561.00			1.41035			0.705175	+	0.709034i	$0.250869\pi$
$108$		0			0
$109$	−936.140			−0.822623			−0.411311	−	0.911495i	$-0.634929\pi$
$109$	−936.140			−0.822623			−0.411311	+	0.911495i	$0.634929\pi$
$110$	13.7837	+	23.8740i	0.0119475	+	0.0206936i
$111$		0			0
$112$	−267.733	+	463.727i	−0.225878	+	0.391233i
$113$	677.490	−	1173.45i	0.564008	−	0.976890i	−0.433134	−	0.901330i	$-0.642592\pi$
$113$	677.490	−	1173.45i	0.564008	−	0.976890i	0.997141	−	0.0755602i	$-0.0240745\pi$
$114$		0			0
$115$	−485.643	−	841.159i	−0.393795	−	0.682074i
$116$	29.8351			0.0238803
$117$		0			0
$118$	86.4153			0.0674167
$119$	−187.601	−	324.935i	−0.144516	−	0.250309i
$120$		0			0
$121$	169.115	−	292.915i	0.127058	−	0.220071i
$122$	66.4490	−	115.093i	0.0493115	−	0.0854101i
$123$		0			0
$124$	−1002.80	−	1736.90i	−0.726244	−	1.25789i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−1182.37			−0.826126			−0.413063	−	0.910702i	$-0.635541\pi$
$127$	−1182.37			−0.826126			−0.413063	+	0.910702i	$0.635541\pi$
$128$	177.474	+	307.393i	0.122552	+	0.212266i
$129$		0			0
$130$	11.7544	−	20.3592i	0.00793022	−	0.0137356i
$131$	1126.87	−	1951.80i	0.751569	−	1.30176i	−0.195494	−	0.980705i	$-0.562631\pi$
$131$	1126.87	−	1951.80i	0.751569	−	1.30176i	0.947062	−	0.321050i	$-0.104036\pi$
$132$		0			0
$133$	381.748	+	661.207i	0.248885	+	0.431082i
$134$	−95.1199			−0.0613217
$135$		0			0
$136$	−123.877			−0.0781059
$137$	236.856	+	410.246i	0.147708	+	0.255837i	0.930380	−	0.366597i	$-0.119477\pi$
$137$	236.856	+	410.246i	0.147708	+	0.255837i	−0.782672	+	0.622434i	$0.786144\pi$
$138$		0			0
$139$	68.5193	−	118.679i	0.0418110	−	0.0724188i	−0.844363	−	0.535772i	$-0.820021\pi$
$139$	68.5193	−	118.679i	0.0418110	−	0.0724188i	0.886174	+	0.463353i	$0.153354\pi$
$140$	−168.626	+	292.069i	−0.101797	+	0.176317i
$141$		0			0
$142$	−81.2110	−	140.662i	−0.0479935	−	0.0831272i
$143$	846.613			0.495086
$144$		0			0
$145$	18.7186			0.0107206
$146$	−53.2600	−	92.2490i	−0.0301906	−	0.0522917i
$147$		0			0
$148$	−247.965	+	429.487i	−0.137720	+	0.238538i
$149$	−71.5553	+	123.937i	−0.0393426	+	0.0681433i	−0.885026	−	0.465541i	$-0.845860\pi$
$149$	−71.5553	+	123.937i	−0.0393426	+	0.0681433i	0.845684	+	0.533685i	$0.179193\pi$
$150$		0			0
$151$	−108.421	−	187.790i	−0.0584314	−	0.101206i	0.835330	−	0.549749i	$-0.185277\pi$
$151$	−108.421	−	187.790i	−0.0584314	−	0.101206i	−0.893761	+	0.448543i	$0.851943\pi$
$152$	252.077			0.134514
$153$		0			0
$154$	46.6644			0.0244177
$155$	−629.159	−	1089.74i	−0.326034	−	0.564708i
$156$		0			0
$157$	−674.215	+	1167.78i	−0.342728	+	0.593622i	−0.984938	−	0.172906i	$-0.944684\pi$
$157$	−674.215	+	1167.78i	−0.342728	+	0.593622i	0.642211	+	0.766528i	$0.278017\pi$
$158$	−53.7938	+	93.1736i	−0.0270861	+	0.0469145i
$159$		0			0
$160$	83.5644	+	144.738i	0.0412897	+	0.0715158i
$161$	−1644.14			−0.804822
$162$		0			0
$163$	1039.85			0.499676			0.249838	−	0.968288i	$-0.419623\pi$
$163$	1039.85			0.499676			0.249838	+	0.968288i	$0.419623\pi$
$164$	814.254	+	1410.33i	0.387699	+	0.671514i
$165$		0			0
$166$	94.0813	−	162.954i	0.0439887	−	0.0761907i
$167$	−1663.52	+	2881.31i	−0.770822	+	1.33510i	0.166291	+	0.986077i	$0.446821\pi$
$167$	−1663.52	+	2881.31i	−0.770822	+	1.33510i	−0.937113	+	0.349026i	$0.886513\pi$
$168$		0			0
$169$	737.513	+	1277.41i	0.335691	+	0.581434i
$170$	−38.7859			−0.0174985
$171$		0			0
$172$	4205.13			1.86418
$173$	−597.127	−	1034.25i	−0.262420	−	0.454525i	0.704464	−	0.709740i	$-0.251187\pi$
$173$	−597.127	−	1034.25i	−0.262420	−	0.454525i	−0.966885	+	0.255214i	$0.917854\pi$
$174$		0			0
$175$	−105.796	+	183.245i	−0.0456998	+	0.0791543i
$176$	−996.702	+	1726.34i	−0.426871	+	0.739362i
$177$		0			0
$178$	131.689	+	228.092i	0.0554523	+	0.0960463i
$179$	−2323.70			−0.970288			−0.485144	−	0.874434i	$-0.661233\pi$
$179$	−2323.70			−0.970288			−0.485144	+	0.874434i	$0.661233\pi$
$180$		0			0
$181$	2527.12			1.03779			0.518893	−	0.854839i	$-0.326344\pi$
$181$	2527.12			1.03779			0.518893	+	0.854839i	$0.326344\pi$
$182$	−19.8972	−	34.4629i	−0.00810372	−	0.0140361i
$183$		0			0
$184$	−271.416	+	470.106i	−0.108745	+	0.188352i
$185$	−155.573	+	269.461i	−0.0618269	+	0.107087i
$186$		0			0
$187$	−698.391	−	1209.65i	−0.273109	−	0.473039i
$188$	1241.05			0.481452
$189$		0			0
$190$	78.9252			0.0301360
$191$	1194.43	+	2068.82i	0.452493	+	0.783741i	0.998540	−	0.0540134i	$-0.0172014\pi$
$191$	1194.43	+	2068.82i	0.452493	+	0.783741i	−0.546047	+	0.837754i	$0.683868\pi$
$192$		0			0
$193$	−1773.99	+	3072.64i	−0.661629	+	1.14597i	0.318559	+	0.947903i	$0.396801\pi$
$193$	−1773.99	+	3072.64i	−0.661629	+	1.14597i	−0.980188	+	0.198072i	$0.936532\pi$
$194$	29.1120	−	50.4235i	0.0107738	−	0.0186608i
$195$		0			0
$196$	−1081.31	−	1872.88i	−0.394063	−	0.682536i
$197$	1239.26			0.448192			0.224096	−	0.974567i	$-0.428057\pi$
$197$	1239.26			0.448192			0.224096	+	0.974567i	$0.428057\pi$
$198$		0			0
$199$	516.657			0.184044			0.0920222	−	0.995757i	$-0.470667\pi$
$199$	516.657			0.184044			0.0920222	+	0.995757i	$0.470667\pi$
$200$	34.9299	+	60.5004i	0.0123496	+	0.0213901i
$201$		0			0
$202$	−43.3074	+	75.0107i	−0.0150847	+	0.0261274i
$203$	15.8429	−	27.4406i	0.00547759	−	0.00948746i
$204$		0			0
$205$	510.864	+	884.843i	0.174050	+	0.301464i
$206$	−110.246			−0.0372873
$207$		0			0
$208$	1699.93			0.566678
$209$	1421.15	+	2461.51i	0.470350	+	0.814670i
$210$		0			0
$211$	8.92159	−	15.4527i	0.00291084	−	0.00504173i	−0.864566	−	0.502519i	$-0.832407\pi$
$211$	8.92159	−	15.4527i	0.00291084	−	0.00504173i	0.867477	+	0.497477i	$0.165740\pi$
$212$	564.607	−	977.928i	0.182912	−	0.316813i
$213$		0			0
$214$	−136.575	−	236.555i	−0.0436266	−	0.0755635i
$215$	2638.31			0.836888
$216$		0			0
$217$	−2130.01			−0.666334
$218$	81.9050	+	141.864i	0.0254464	+	0.0440744i
$219$		0			0
$220$	−627.753	+	1087.30i	−0.192378	+	0.333208i
$221$	−595.573	+	1031.56i	−0.181279	+	0.313984i
$222$		0			0
$223$	−494.777	−	856.978i	−0.148577	−	0.257343i	0.782125	−	0.623122i	$-0.214136\pi$
$223$	−494.777	−	856.978i	−0.148577	−	0.257343i	−0.930702	+	0.365779i	$0.880803\pi$
$224$	282.906			0.0843860
$225$		0			0
$226$	−237.101			−0.0697863
$227$	−1713.57	−	2967.98i	−0.501028	−	0.867806i	−0.999999	−	0.00118754i	$-0.999622\pi$
$227$	−1713.57	−	2967.98i	−0.501028	−	0.867806i	0.498971	−	0.866619i	$-0.333711\pi$
$228$		0			0
$229$	−549.805	+	952.290i	−0.158656	+	0.274800i	−0.934384	−	0.356267i	$-0.884049\pi$
$229$	−549.805	+	952.290i	−0.158656	+	0.274800i	0.775728	+	0.631067i	$0.217383\pi$
$230$	−84.9801	+	147.190i	−0.0243627	+	0.0421974i
$231$		0			0
$232$	−5.23071	−	9.05985i	−0.00148023	−	0.00256383i
$233$	−4459.91			−1.25399			−0.626993	−	0.779025i	$-0.715715\pi$
$233$	−4459.91			−1.25399			−0.626993	+	0.779025i	$0.715715\pi$
$234$		0			0
$235$	778.637			0.216139
$236$	1967.82	+	3408.37i	0.542772	+	0.940109i
$237$		0			0
$238$	−32.8273	+	56.8586i	−0.00894067	+	0.0154857i
$239$	3272.23	−	5667.66i	0.885618	−	1.53394i	0.0406148	−	0.999175i	$-0.487068\pi$
$239$	3272.23	−	5667.66i	0.885618	−	1.53394i	0.845003	−	0.534761i	$-0.179598\pi$
$240$		0			0
$241$	105.162	+	182.147i	0.0281083	+	0.0486851i	0.879737	−	0.475460i	$-0.157718\pi$
$241$	105.162	+	182.147i	0.0281083	+	0.0486851i	−0.851629	+	0.524145i	$0.824385\pi$
$242$	−59.1849			−0.0157213
$243$		0			0
$244$	6052.61			1.58803
$245$	−678.414	−	1175.05i	−0.176907	−	0.306412i
$246$		0			0
$247$	1211.93	−	2099.12i	0.312199	−	0.540744i
$248$	−351.624	+	609.031i	−0.0900329	+	0.155942i
$249$		0			0
$250$	10.9365	+	18.9426i	0.00276675	+	0.00479215i
$251$	−816.143			−0.205237			−0.102618	−	0.994721i	$-0.532722\pi$
$251$	−816.143			−0.205237			−0.102618	+	0.994721i	$0.532722\pi$
$252$		0			0
$253$	−6120.71			−1.52097
$254$	103.448	+	179.177i	0.0255547	+	0.0442621i
$255$		0			0
$256$	−1970.06	+	3412.25i	−0.480972	+	0.833069i
$257$	−2086.17	+	3613.36i	−0.506350	+	0.877023i	0.493623	+	0.869676i	$0.335672\pi$
$257$	−2086.17	+	3613.36i	−0.506350	+	0.877023i	−0.999973	+	0.00734758i	$0.997661\pi$
$258$		0			0
$259$	263.346	+	456.128i	0.0631795	+	0.109430i
$260$	1070.67			0.255385
$261$		0			0
$262$	−394.371			−0.0929937
$263$	−1408.52	−	2439.64i	−0.330241	−	0.571994i	0.652318	−	0.757945i	$-0.273797\pi$
$263$	−1408.52	−	2439.64i	−0.330241	−	0.571994i	−0.982559	+	0.185951i	$0.940463\pi$
$264$		0			0
$265$	354.235	−	613.554i	0.0821151	−	0.142228i
$266$	66.8001	−	115.701i	0.0153976	−	0.0266695i
$267$		0			0
$268$	−2166.04	−	3751.69i	−0.493701	−	0.855115i
$269$	102.610			0.0232573			0.0116287	−	0.999932i	$-0.496298\pi$
$269$	102.610			0.0232573			0.0116287	+	0.999932i	$0.496298\pi$
$270$		0			0
$271$	−3337.27			−0.748061			−0.374031	−	0.927416i	$-0.622025\pi$
$271$	−3337.27			−0.748061			−0.374031	+	0.927416i	$0.622025\pi$
$272$	−1402.31	−	2428.88i	−0.312602	−	0.541443i
$273$		0			0
$274$	41.4461	−	71.7867i	0.00913814	−	0.0158277i
$275$	−393.853	+	682.174i	−0.0863645	+	0.149588i
$276$		0			0
$277$	−316.941	−	548.959i	−0.0687479	−	0.119075i	0.829603	−	0.558354i	$-0.188567\pi$
$277$	−316.941	−	548.959i	−0.0687479	−	0.119075i	−0.898350	+	0.439280i	$0.855234\pi$
$278$	−23.9796			−0.00517339
$279$		0			0
$280$	118.255			0.0252396
$281$	−3101.20	−	5371.44i	−0.658370	−	1.14033i	−0.981037	−	0.193818i	$-0.937913\pi$
$281$	−3101.20	−	5371.44i	−0.658370	−	1.14033i	0.322667	−	0.946513i	$-0.395421\pi$
$282$		0			0
$283$	3740.06	−	6477.98i	0.785596	−	1.36069i	−0.143047	−	0.989716i	$-0.545690\pi$
$283$	3740.06	−	6477.98i	0.785596	−	1.36069i	0.928642	−	0.370976i	$-0.120977\pi$
$284$	3698.62	−	6406.19i	0.772791	−	1.33851i
$285$		0			0
$286$	−74.0722	−	128.297i	−0.0153146	−	0.0265257i
$287$	1729.52			0.355716
$288$		0			0
$289$	−2947.79			−0.599998
$290$	−1.63773	−	2.83663i	−0.000331623	−	0.000574389i
$291$		0			0
$292$	2425.64	−	4201.33i	0.486129	−	0.842000i
$293$	−2418.26	+	4188.54i	−0.482171	+	0.835144i	−0.999791	−	0.0204666i	$-0.993485\pi$
$293$	−2418.26	+	4188.54i	−0.482171	+	0.835144i	0.517620	+	0.855611i	$0.326818\pi$
$294$		0			0
$295$	1234.61	+	2138.41i	0.243668	+	0.422045i
$296$	173.893			0.0341464
$297$		0			0
$298$	25.0422			0.00486796
$299$	2609.81	+	4520.31i	0.504779	+	0.874303i
$300$		0			0
$301$	2232.99	−	3867.65i	0.427599	−	0.740623i
$302$	−18.9719	+	32.8604i	−0.00361494	+	0.00626126i
$303$		0			0
$304$	2853.56	+	4942.51i	0.538365	+	0.932475i
$305$	3797.42			0.712916
$306$		0			0
$307$	−5611.86			−1.04328			−0.521638	−	0.853167i	$-0.674679\pi$
$307$	−5611.86			−1.04328			−0.521638	+	0.853167i	$0.674679\pi$
$308$	1062.63	+	1840.52i	0.196587	+	0.340498i
$309$		0			0
$310$	−110.093	+	190.687i	−0.0201706	+	0.0349364i
$311$	5460.70	−	9458.21i	0.995653	−	1.72452i	0.417163	−	0.908831i	$-0.363024\pi$
$311$	5460.70	−	9458.21i	0.995653	−	1.72452i	0.578489	−	0.815690i	$-0.303642\pi$
$312$		0			0
$313$	−2490.36	−	4313.44i	−0.449724	−	0.778946i	0.548643	−	0.836056i	$-0.315144\pi$
$313$	−2490.36	−	4313.44i	−0.449724	−	0.778946i	−0.998368	+	0.0571109i	$0.981811\pi$
$314$	235.955			0.0424067
$315$		0			0
$316$	−4899.89			−0.872280
$317$	−1878.06	−	3252.90i	−0.332752	−	0.576344i	0.650298	−	0.759679i	$-0.274644\pi$
$317$	−1878.06	−	3252.90i	−0.332752	−	0.576344i	−0.983050	+	0.183335i	$0.941311\pi$
$318$		0			0
$319$	58.9789	−	102.154i	0.0103517	−	0.0179296i
$320$	−1250.70	+	2166.27i	−0.218488	+	0.378432i
$321$		0			0
$322$	143.849	+	249.155i	0.0248957	+	0.0431206i
$323$	−3998.99			−0.688885
$324$		0			0
$325$	671.739			0.114650
$326$	−90.9788	−	157.580i	−0.0154566	−	0.0267716i
$327$		0			0
$328$	285.511	−	494.520i	0.0480632	−	0.0832479i
$329$	659.016	−	1141.45i	0.110434	−	0.191277i
$330$		0			0
$331$	453.477	+	785.445i	0.0753031	+	0.130429i	0.901218	−	0.433366i	$-0.142674\pi$
$331$	453.477	+	785.445i	0.0753031	+	0.130429i	−0.825915	+	0.563795i	$0.809341\pi$
$332$	8569.55			1.41661
$333$		0			0
$334$	582.182			0.0953759
$335$	−1358.98	−	2353.81i	−0.221638	−	0.383888i
$336$		0			0
$337$	−4939.35	+	8555.20i	−0.798408	+	1.38288i	0.122245	+	0.992500i	$0.460991\pi$
$337$	−4939.35	+	8555.20i	−0.798408	+	1.38288i	−0.920653	+	0.390383i	$0.872343\pi$
$338$	129.053	−	223.527i	0.0207680	−	0.0359712i
$339$		0			0
$340$	−883.220	−	1529.78i	−0.140880	−	0.244012i
$341$	−7929.49			−1.25925
$342$		0			0
$343$	−5199.81			−0.818553
$344$	−737.247	−	1276.95i	−0.115551	−	0.200141i
$345$		0			0
$346$	−104.488	+	180.979i	−0.0162350	+	0.0281199i
$347$	−1754.86	+	3039.50i	−0.271486	+	0.470228i	−0.969243	−	0.246107i	$-0.920848\pi$
$347$	−1754.86	+	3039.50i	−0.271486	+	0.470228i	0.697757	+	0.716335i	$0.254182\pi$
$348$		0			0
$349$	5196.48	+	9000.57i	0.797024	+	1.38049i	0.921546	+	0.388269i	$0.126927\pi$
$349$	5196.48	+	9000.57i	0.797024	+	1.38049i	−0.124522	+	0.992217i	$0.539740\pi$
$350$	37.0255			0.00565456
$351$		0			0
$352$	1053.19			0.159475
$353$	4042.70	+	7002.16i	0.609550	+	1.05577i	0.991315	+	0.131512i	$0.0419830\pi$
$353$	4042.70	+	7002.16i	0.609550	+	1.05577i	−0.381765	+	0.924259i	$0.624684\pi$
$354$		0			0
$355$	2320.52	−	4019.26i	0.346930	−	0.600901i
$356$	−5997.56	+	10388.1i	−0.892893	+	1.54654i
$357$		0			0
$358$	203.306	+	352.136i	0.0300141	+	0.0519860i
$359$	8189.49			1.20397			0.601984	−	0.798508i	$-0.294377\pi$
$359$	8189.49			1.20397			0.601984	+	0.798508i	$0.294377\pi$
$360$		0			0
$361$	1278.52			0.186400
$362$	−221.103	−	382.962i	−0.0321020	−	0.0556024i
$363$		0			0
$364$	906.184	−	1569.56i	0.130486	−	0.226008i
$365$	1521.85	−	2635.92i	0.218239	−	0.378001i
$366$		0			0
$367$	4497.33	+	7789.60i	0.639669	+	1.10794i	0.985505	+	0.169645i	$0.0542621\pi$
$367$	4497.33	+	7789.60i	0.639669	+	1.10794i	−0.345836	+	0.938295i	$0.612405\pi$
$368$	−12289.9			−1.74091
$369$		0			0
$370$	54.4459			0.00765001
$371$	−599.629	−	1038.59i	−0.0839116	−	0.145339i
$372$		0			0
$373$	464.934	−	805.288i	0.0645398	−	0.111786i	−0.831950	−	0.554851i	$-0.812775\pi$
$373$	464.934	−	805.288i	0.0645398	−	0.111786i	0.896490	+	0.443064i	$0.146109\pi$
$374$	−122.208	+	211.670i	−0.0168963	+	0.0292652i
$375$		0			0
$376$	−217.582	−	376.863i	−0.0298429	−	0.0516894i
$377$	−100.592			−0.0137420
$378$		0			0
$379$	3449.71			0.467546			0.233773	−	0.972291i	$-0.424893\pi$
$379$	3449.71			0.467546			0.233773	+	0.972291i	$0.424893\pi$
$380$	1797.26	+	3112.94i	0.242625	+	0.420238i
$381$		0			0
$382$	209.007	−	362.012i	0.0279941	−	0.0484872i
$383$	−2673.07	+	4629.89i	−0.356625	+	0.617692i	−0.987395	−	0.158278i	$-0.949406\pi$
$383$	−2673.07	+	4629.89i	−0.356625	+	0.617692i	0.630770	+	0.775970i	$0.282739\pi$
$384$		0			0
$385$	666.692	+	1154.75i	0.0882540	+	0.152860i
$386$	620.841			0.0818652
$387$		0			0
$388$	2651.72			0.346960
$389$	3861.72	+	6688.70i	0.503334	+	0.871801i	0.999993	+	0.00385448i	$0.00122692\pi$
$389$	3861.72	+	6688.70i	0.503334	+	0.871801i	−0.496658	+	0.867946i	$0.665440\pi$
$390$		0			0
$391$	4305.78	−	7457.83i	0.556912	−	0.964600i
$392$	−379.151	+	656.709i	−0.0488521	+	0.0846144i
$393$		0			0
$394$	−108.426	−	187.799i	−0.0138640	−	0.0240132i
$395$	−3074.20			−0.391594
$396$		0			0
$397$	7125.03			0.900744			0.450372	−	0.892841i	$-0.351291\pi$
$397$	7125.03			0.900744			0.450372	+	0.892841i	$0.351291\pi$
$398$	−45.2035	−	78.2948i	−0.00569308	−	0.00986071i
$399$		0			0
$400$	−790.826	+	1369.75i	−0.0988532	+	0.171219i
$401$	−896.547	+	1552.86i	−0.111649	+	0.193382i	−0.916435	−	0.400183i	$-0.868947\pi$
$401$	−896.547	+	1552.86i	−0.111649	+	0.193382i	0.804786	+	0.593565i	$0.202280\pi$
$402$		0			0
$403$	3381.05	+	5856.15i	0.417921	+	0.723860i
$404$	−3944.73			−0.485786
$405$		0			0
$406$	−5.54451			−0.000677757
$407$	980.369	+	1698.05i	0.119398	+	0.206804i
$408$		0			0
$409$	−1569.87	+	2719.09i	−0.189792	+	0.328729i	−0.945181	−	0.326548i	$-0.894115\pi$
$409$	−1569.87	+	2719.09i	−0.189792	+	0.328729i	0.755389	+	0.655277i	$0.227448\pi$
$410$	89.3934	−	154.834i	0.0107679	−	0.0186505i
$411$		0			0
$412$	−2510.48	−	4348.27i	−0.300200	−	0.519961i
$413$	4179.77			0.497997
$414$		0			0
$415$	5376.55			0.635962
$416$	−449.068	−	777.808i	−0.0529263	−	0.0916711i
$417$		0			0
$418$	248.680	−	430.726i	0.0290989	−	0.0504007i
$419$	1228.70	−	2128.17i	0.143260	−	0.248133i	−0.785463	−	0.618909i	$-0.787575\pi$
$419$	1228.70	−	2128.17i	0.143260	−	0.248133i	0.928722	+	0.370776i	$0.120908\pi$
$420$		0			0
$421$	1339.33	+	2319.80i	0.155048	+	0.268551i	0.933076	−	0.359678i	$-0.117113\pi$
$421$	1339.33	+	2319.80i	0.155048	+	0.268551i	−0.778029	+	0.628229i	$0.783780\pi$
$422$	−3.12228			−0.000360167
$423$		0			0
$424$	−395.949			−0.0453514
$425$	−554.134	−	959.787i	−0.0632457	−	0.109545i
$426$		0			0
$427$	3214.03	−	5566.86i	0.364257	−	0.630911i
$428$	6220.09	−	10773.5i	0.702476	−	1.21672i
$429$		0			0
$430$	−230.831	−	399.812i	−0.0258876	−	0.0448387i
$431$	9472.42			1.05863			0.529316	−	0.848425i	$-0.322449\pi$
$431$	9472.42			1.05863			0.529316	+	0.848425i	$0.322449\pi$
$432$		0			0
$433$	−4238.21			−0.470382			−0.235191	−	0.971949i	$-0.575572\pi$
$433$	−4238.21			−0.470382			−0.235191	+	0.971949i	$0.575572\pi$
$434$	186.360	+	322.784i	0.0206119	+	0.0357008i
$435$		0			0
$436$	−3730.23	+	6460.94i	−0.409737	+	0.709686i
$437$	−8761.80	+	15175.9i	−0.959116	+	1.66124i
$438$		0			0
$439$	−2429.47	−	4207.96i	−0.264128	−	0.457483i	0.703207	−	0.710985i	$-0.251751\pi$
$439$	−2429.47	−	4207.96i	−0.264128	−	0.457483i	−0.967335	+	0.253503i	$0.918417\pi$
$440$	440.233			0.0476984
$441$		0			0
$442$	208.432			0.0224301
$443$	1167.88	+	2022.82i	0.125254	+	0.216946i	0.921832	−	0.387589i	$-0.126692\pi$
$443$	1167.88	+	2022.82i	0.125254	+	0.216946i	−0.796578	+	0.604535i	$0.793359\pi$
$444$		0			0
$445$	−3762.88	+	6517.49i	−0.400848	+	0.694289i
$446$	−86.5783	+	149.958i	−0.00919193	+	0.0159209i
$447$		0			0
$448$	2117.11	+	3666.94i	0.223268	+	0.386712i
$449$	−13290.5			−1.39692			−0.698460	−	0.715649i	$-0.746131\pi$
$449$	−13290.5			−1.39692			−0.698460	+	0.715649i	$0.746131\pi$
$450$		0			0
$451$	6438.58			0.672241
$452$	−5399.17	−	9351.64i	−0.561849	−	0.973151i
$453$		0			0
$454$	−299.848	+	519.351i	−0.0309968	+	0.0536880i
$455$	568.541	−	984.742i	0.0585794	−	0.101462i
$456$		0			0
$457$	−2587.31	−	4481.35i	−0.264834	−	0.458706i	0.702686	−	0.711500i	$-0.251984\pi$
$457$	−2587.31	−	4481.35i	−0.264834	−	0.458706i	−0.967520	+	0.252794i	$0.918650\pi$
$458$	192.415			0.0196309
$459$		0			0
$460$	−7740.55			−0.784576
$461$	3170.44	+	5491.37i	0.320309	+	0.554791i	0.980552	−	0.196261i	$-0.0628801\pi$
$461$	3170.44	+	5491.37i	0.320309	+	0.554791i	−0.660243	+	0.751052i	$0.729547\pi$
$462$		0			0
$463$	−1591.40	+	2756.38i	−0.159737	+	0.276673i	−0.934774	−	0.355243i	$-0.884398\pi$
$463$	−1591.40	+	2756.38i	−0.159737	+	0.276673i	0.775036	+	0.631916i	$0.217731\pi$
$464$	118.425	−	205.118i	0.0118486	−	0.0205223i
$465$		0			0
$466$	390.208	+	675.860i	0.0387898	+	0.0671859i
$467$	8576.23			0.849808			0.424904	−	0.905238i	$-0.360308\pi$
$467$	8576.23			0.849808			0.424904	+	0.905238i	$0.360308\pi$
$468$		0			0
$469$	−4600.79			−0.452974
$470$	−68.1247	−	117.995i	−0.00668587	−	0.0115803i
$471$		0			0
$472$	690.000	−	1195.11i	0.0672877	−	0.116546i
$473$	8312.84	−	14398.3i	0.808086	−	1.39965i
$474$		0			0
$475$	1127.60	+	1953.06i	0.108922	+	0.188658i
$476$	−2990.13			−0.287925
$477$		0			0
$478$	−1145.18			−0.109580
$479$	1458.82	+	2526.76i	0.139155	+	0.241024i	0.927177	−	0.374623i	$-0.122228\pi$
$479$	1458.82	+	2526.76i	0.139155	+	0.241024i	−0.788022	+	0.615647i	$0.788895\pi$
$480$		0			0
$481$	836.037	−	1448.06i	0.0792516	−	0.137268i
$482$	18.4018	−	31.8729i	0.00173896	−	0.00301197i
$483$		0			0
$484$	−1347.74	−	2334.35i	−0.126572	−	0.219229i
$485$	1663.69			0.155761
$486$		0			0
$487$	−14061.0			−1.30834			−0.654172	−	0.756346i	$-0.726983\pi$
$487$	−14061.0			−1.30834			−0.654172	+	0.756346i	$0.726983\pi$
$488$	−1061.15	−	1837.96i	−0.0984343	−	0.170493i
$489$		0			0
$490$	−118.712	+	205.615i	−0.0109446	+	0.0189566i
$491$	−466.331	+	807.709i	−0.0428620	+	0.0742391i	−0.886661	−	0.462421i	$-0.846981\pi$
$491$	−466.331	+	807.709i	−0.0428620	+	0.0742391i	0.843799	+	0.536660i	$0.180314\pi$
$492$		0			0
$493$	82.9806	+	143.727i	0.00758065	+	0.0131301i
$494$	−424.137			−0.0386292
$495$		0			0
$496$	−15921.8			−1.44135
$497$	−3928.04	−	6803.57i	−0.354521	−	0.614048i
$498$		0			0
$499$	7215.39	−	12497.4i	0.647305	−	1.12117i	−0.336459	−	0.941698i	$-0.609229\pi$
$499$	7215.39	−	12497.4i	0.647305	−	1.12117i	0.983764	−	0.179467i	$-0.0574374\pi$
$500$	−498.086	+	862.711i	−0.0445502	+	0.0771632i
$501$		0			0
$502$	71.4062	+	123.679i	0.00634864	+	0.0109962i
$503$	3230.55			0.286368			0.143184	−	0.989696i	$-0.454266\pi$
$503$	3230.55			0.286368			0.143184	+	0.989696i	$0.454266\pi$
$504$		0			0
$505$	−2474.93			−0.218085
$506$	535.515	+	927.539i	0.0470485	+	0.0814904i
$507$		0			0
$508$	−4711.36	+	8160.32i	−0.411482	+	0.712708i
$509$	−180.378	+	312.424i	−0.0157075	+	0.0272062i	−0.873772	−	0.486335i	$-0.838333\pi$
$509$	−180.378	+	312.424i	−0.0157075	+	0.0272062i	0.858065	+	0.513541i	$0.171667\pi$
$510$		0			0
$511$	−2576.10	−	4461.93i	−0.223013	−	0.386270i
$512$	3529.04			0.304615
$513$		0			0
$514$	730.096			0.0626521
$515$	−1575.08	−	2728.11i	−0.134769	−	0.233427i
$516$		0			0
$517$	2453.35	−	4249.33i	0.208701	−	0.361480i
$518$	46.0814	−	79.8154i	0.00390869	−	0.00677005i
$519$		0			0
$520$	−187.710	−	325.124i	−0.0158301	−	0.0274185i
$521$	11698.8			0.983747			0.491873	−	0.870667i	$-0.336312\pi$
$521$	11698.8			0.983747			0.491873	+	0.870667i	$0.336312\pi$
$522$		0			0
$523$	18557.3			1.55154			0.775770	−	0.631015i	$-0.217362\pi$
$523$	18557.3			1.55154			0.775770	+	0.631015i	$0.217362\pi$
$524$	−8980.49	−	15554.7i	−0.748692	−	1.29677i
$525$		0			0
$526$	−246.470	+	426.899i	−0.0204308	+	0.0353872i
$527$	5578.21	−	9661.75i	0.461083	−	0.798619i
$528$		0			0
$529$	−12784.5	−	22143.3i	−1.05075	−	1.81995i
$530$	−123.971			−0.0101603
$531$		0			0
$532$	6084.59			0.495866
$533$	−2745.34	−	4755.07i	−0.223103	−	0.386426i
$534$		0			0
$535$	3902.50	−	6759.32i	0.315364	−	0.546226i
$536$	−759.503	+	1315.50i	−0.0612044	+	0.106009i
$537$		0			0
$538$	−8.97756	−	15.5496i	−0.000719424	−	0.00124608i
$539$	−8550.26			−0.683276
$540$		0			0
$541$	22755.3			1.80837			0.904185	−	0.427140i	$-0.140479\pi$
$541$	22755.3			1.80837			0.904185	+	0.427140i	$0.140479\pi$
$542$	291.985	+	505.733i	0.0231399	+	0.0400795i
$543$		0			0
$544$	−740.893	+	1283.26i	−0.0583925	+	0.101139i
$545$	−2340.35	+	4053.60i	−0.183944	+	0.318601i
$546$		0			0
$547$	−2899.05	−	5021.30i	−0.226608	−	0.392496i	0.730193	−	0.683241i	$-0.239430\pi$
$547$	−2899.05	−	5021.30i	−0.226608	−	0.392496i	−0.956801	+	0.290745i	$0.906097\pi$
$548$	3775.18			0.294284
$549$		0			0
$550$	137.837			0.0106861
$551$	−168.857	−	292.468i	−0.0130554	−	0.0226127i
$552$		0			0
$553$	−2601.92	+	4506.65i	−0.200081	+	0.346550i
$554$	−55.4599	+	96.0593i	−0.00425318	+	0.00736673i
$555$		0			0
$556$	−546.056	−	945.797i	−0.0416510	−	0.0721416i
$557$	−15740.3			−1.19738			−0.598688	−	0.800982i	$-0.704311\pi$
$557$	−15740.3			−1.19738			−0.598688	+	0.800982i	$0.704311\pi$
$558$		0			0
$559$	−14178.0			−1.07275
$560$	1338.66	+	2318.64i	0.101016	+	0.174965i
$561$		0			0
$562$	−542.662	+	939.919i	−0.0407310	+	0.0705482i
$563$	1909.56	−	3307.45i	0.142946	−	0.247589i	−0.785659	−	0.618660i	$-0.787676\pi$
$563$	1909.56	−	3307.45i	0.142946	−	0.247589i	0.928605	+	0.371071i	$0.121009\pi$
$564$		0			0
$565$	−3387.45	−	5867.23i	−0.252232	−	0.436878i
$566$	−1308.91			−0.0972040
$567$		0			0
$568$	−2593.78			−0.191607
$569$	4445.56	+	7699.93i	0.327535	+	0.567308i	0.982022	−	0.188766i	$-0.0604487\pi$
$569$	4445.56	+	7699.93i	0.327535	+	0.567308i	−0.654487	+	0.756073i	$0.727115\pi$
$570$		0			0
$571$	−4193.31	+	7263.03i	−0.307329	+	0.532309i	−0.977777	−	0.209647i	$-0.932768\pi$
$571$	−4193.31	+	7263.03i	−0.307329	+	0.532309i	0.670448	+	0.741956i	$0.266102\pi$
$572$	3373.49	−	5843.06i	0.246596	−	0.427116i
$573$		0			0
$574$	−151.320	−	262.094i	−0.0110034	−	0.0190585i
$575$	−4856.43			−0.352221
$576$		0			0
$577$	16922.3			1.22095			0.610473	−	0.792037i	$-0.290979\pi$
$577$	16922.3			1.22095			0.610473	+	0.792037i	$0.290979\pi$
$578$	257.909	+	446.711i	0.0185599	+	0.0321466i
$579$		0			0
$580$	74.5877	−	129.190i	0.00533980	−	0.00924880i
$581$	4550.56	−	7881.80i	0.324938	−	0.562809i
$582$		0			0
$583$	−2232.27	−	3866.40i	−0.158578	−	0.274666i
$584$	−1701.06			−0.120531
$585$		0			0
$586$	846.315			0.0596603
$587$	7619.29	+	13197.0i	0.535744	+	0.927936i	0.999127	+	0.0417777i	$0.0133021\pi$
$587$	7619.29	+	13197.0i	0.535744	+	0.927936i	−0.463383	+	0.886158i	$0.653365\pi$
$588$		0			0
$589$	−11351.1	+	19660.6i	−0.794079	+	1.37539i
$590$	216.038	−	374.189i	0.0150748	−	0.0261104i
$591$		0			0
$592$	1968.50	+	3409.55i	0.136664	+	0.236709i
$593$	16960.2			1.17449			0.587245	−	0.809409i	$-0.300213\pi$
$593$	16960.2			1.17449			0.587245	+	0.809409i	$0.300213\pi$
$594$		0			0
$595$	−1876.01			−0.129259
$596$	570.252	+	987.705i	0.0391920	+	0.0678825i
$597$		0			0
$598$	456.676	−	790.986i	0.0312289	−	0.0540900i
$599$	−12456.1	+	21574.5i	−0.849651	+	1.47164i	0.0318690	+	0.999492i	$0.489854\pi$
$599$	−12456.1	+	21574.5i	−0.849651	+	1.47164i	−0.881520	+	0.472147i	$0.843479\pi$
$600$		0			0
$601$	2175.63	+	3768.31i	0.147664	+	0.255761i	0.930364	−	0.366638i	$-0.119491\pi$
$601$	2175.63	+	3768.31i	0.147664	+	0.255761i	−0.782700	+	0.622399i	$0.786158\pi$
$602$	−781.476			−0.0529080
$603$		0			0
$604$	−1728.09			−0.116416
$605$	−845.573	−	1464.58i	−0.0568222	−	0.0984190i
$606$		0			0
$607$	−13911.8	+	24096.0i	−0.930254	+	1.61125i	−0.147369	+	0.989082i	$0.547081\pi$
$607$	−13911.8	+	24096.0i	−0.930254	+	1.61125i	−0.782885	+	0.622166i	$0.786253\pi$
$608$	1507.64	−	2611.31i	0.100564	−	0.174182i
$609$		0			0
$610$	−332.245	−	575.465i	−0.0220528	−	0.0381965i
$611$	−4184.33			−0.277054
$612$		0			0
$613$	20034.6			1.32005			0.660024	−	0.751244i	$-0.270546\pi$
$613$	20034.6			1.32005			0.660024	+	0.751244i	$0.270546\pi$
$614$	490.994	+	850.427i	0.0322719	+	0.0558965i
$615$		0			0
$616$	372.600	−	645.363i	0.0243709	−	0.0422117i
$617$	3776.95	−	6541.86i	0.246441	−	0.426848i	−0.716095	−	0.698003i	$-0.754072\pi$
$617$	3776.95	−	6541.86i	0.246441	−	0.426848i	0.962536	+	0.271155i	$0.0874055\pi$
$618$		0			0
$619$	−6192.54	−	10725.8i	−0.402099	−	0.696456i	0.591880	−	0.806026i	$-0.298386\pi$
$619$	−6192.54	−	10725.8i	−0.402099	−	0.696456i	−0.993979	+	0.109570i	$0.965053\pi$
$620$	−10028.0			−0.649573
$621$		0			0
$622$	−1911.08			−0.123195
$623$	6369.58	+	11032.4i	0.409618	+	0.709479i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−435.775	+	754.785i	−0.0278228	+	0.0481906i
$627$		0			0
$628$	5373.08	+	9306.45i	0.341416	+	0.591350i
$629$	−2758.67			−0.174873
$630$		0			0
$631$	−1325.17			−0.0836043			−0.0418022	−	0.999126i	$-0.513310\pi$
$631$	−1325.17			−0.0836043			−0.0418022	+	0.999126i	$0.513310\pi$
$632$	859.053	+	1487.92i	0.0540685	+	0.0936494i
$633$		0			0
$634$	−328.632	+	569.207i	−0.0205862	+	0.0356563i
$635$	−2955.91	+	5119.79i	−0.184727	+	0.319957i
$636$		0			0
$637$	3645.74	+	6314.60i	0.226765	+	0.392769i
$638$	−20.6408			−0.00128084
$639$		0			0
$640$	1774.74			0.109613
$641$	−11255.8	−	19495.6i	−0.693568	−	1.20129i	−0.970661	−	0.240451i	$-0.922705\pi$
$641$	−11255.8	−	19495.6i	−0.693568	−	1.20129i	0.277094	−	0.960843i	$-0.410629\pi$
$642$		0			0
$643$	−2807.31	+	4862.40i	−0.172176	+	0.298218i	−0.939180	−	0.343424i	$-0.888413\pi$
$643$	−2807.31	+	4862.40i	−0.172176	+	0.298218i	0.767004	+	0.641642i	$0.221747\pi$
$644$	−6551.38	+	11347.3i	−0.400871	+	0.694328i
$645$		0			0
$646$	349.881	+	606.012i	0.0213094	+	0.0369090i
$647$	11753.6			0.714188			0.357094	−	0.934068i	$-0.383768\pi$
$647$	11753.6			0.714188			0.357094	+	0.934068i	$0.383768\pi$
$648$		0			0
$649$	15560.2			0.941127
$650$	−58.7720	−	101.796i	−0.00354650	−	0.00614273i
$651$		0			0
$652$	4143.48	−	7176.71i	0.248882	−	0.431076i
$653$	−12929.1	+	22393.9i	−0.774816	+	1.34202i	0.160082	+	0.987104i	$0.448824\pi$
$653$	−12929.1	+	22393.9i	−0.774816	+	1.34202i	−0.934898	+	0.354916i	$0.884509\pi$
$654$		0			0
$655$	−5634.37	−	9759.02i	−0.336112	−	0.582163i
$656$	12928.1			0.769450
$657$		0			0
$658$	−230.635			−0.0136643
$659$	−8847.75	−	15324.8i	−0.523004	−	0.905869i	−0.999642	−	0.0267695i	$-0.991478\pi$
$659$	−8847.75	−	15324.8i	−0.523004	−	0.905869i	0.476638	−	0.879100i	$-0.341855\pi$
$660$		0			0
$661$	−3115.05	+	5395.42i	−0.183300	+	0.317485i	−0.943002	−	0.332786i	$-0.892011\pi$
$661$	−3115.05	+	5395.42i	−0.183300	+	0.317485i	0.759702	+	0.650271i	$0.225345\pi$
$662$	79.3515	−	137.441i	0.00465873	−	0.00806916i
$663$		0			0
$664$	−1502.42	−	2602.27i	−0.0878091	−	0.152090i
$665$	3817.48			0.222610
$666$		0			0
$667$	727.243			0.0422174
$668$	13257.2	+	22962.2i	0.767872	+	1.32999i
$669$		0			0
$670$	−237.800	+	411.881i	−0.0137120	+	0.0237498i
$671$	11965.0	−	20724.0i	0.688381	−	1.19231i
$672$		0			0
$673$	3025.84	+	5240.91i	0.173310	+	0.300182i	0.939575	−	0.342343i	$-0.111220\pi$
$673$	3025.84	+	5240.91i	0.173310	+	0.300182i	−0.766265	+	0.642524i	$0.777887\pi$
$674$	1728.62			0.0987892
$675$		0			0
$676$	11755.0			0.668812
$677$	14049.3	+	24334.1i	0.797576	+	1.38144i	0.921190	+	0.389112i	$0.127218\pi$
$677$	14049.3	+	24334.1i	0.797576	+	1.38144i	−0.123614	+	0.992330i	$0.539449\pi$
$678$		0			0
$679$	1408.10	−	2438.90i	0.0795846	−	0.137845i
$680$	−309.694	+	536.405i	−0.0174650	+	0.0302503i
$681$		0			0
$682$	693.769	+	1201.64i	0.0389528	+	0.0674682i
$683$	8335.71			0.466994			0.233497	−	0.972358i	$-0.424983\pi$
$683$	8335.71			0.466994			0.233497	+	0.972358i	$0.424983\pi$
$684$		0			0
$685$	2368.56			0.132114
$686$	454.944	+	787.986i	0.0253205	+	0.0438563i
$687$		0			0
$688$	16691.5	−	28910.6i	0.924939	−	1.60204i
$689$	−1903.63	+	3297.18i	−0.105258	+	0.182312i
$690$		0			0
$691$	8442.55	+	14622.9i	0.464790	+	0.805039i	0.999192	−	0.0401909i	$-0.0127966\pi$
$691$	8442.55	+	14622.9i	0.464790	+	0.805039i	−0.534402	+	0.845230i	$0.679463\pi$
$692$	−9517.46			−0.522832
$693$		0			0
$694$	614.146			0.0335917
$695$	−342.596	−	593.394i	−0.0186984	−	0.0323867i
$696$		0			0
$697$	−4529.39	+	7845.14i	−0.246145	+	0.426335i
$698$	909.305	−	1574.96i	0.0493090	−	0.0854057i
$699$		0			0
$700$	843.132	+	1460.35i	0.0455248	+	0.0788514i
$701$	−16875.2			−0.909226			−0.454613	−	0.890689i	$-0.650222\pi$
$701$	−16875.2			−0.909226			−0.454613	+	0.890689i	$0.650222\pi$
$702$		0			0
$703$	5613.59			0.301167
$704$	7881.47	+	13651.1i	0.421938	+	0.730817i
$705$		0			0
$706$	707.410	−	1225.27i	0.0377106	−	0.0653168i
$707$	−2094.71	+	3628.14i	−0.111428	+	0.192999i
$708$		0			0
$709$	9503.71	+	16460.9i	0.503412	+	0.871936i	0.999992	+	0.00394482i	$0.00125568\pi$
$709$	9503.71	+	16460.9i	0.503412	+	0.871936i	−0.496580	+	0.867991i	$0.665411\pi$
$710$	−812.110			−0.0429267
$711$		0			0
$712$	4205.99			0.221385
$713$	−24443.8	−	42337.9i	−1.28391	−	2.22379i
$714$		0			0
$715$	2116.53	−	3665.94i	0.110705	−	0.191746i
$716$	−9259.23	+	16037.4i	−0.483287	+	0.837078i
$717$		0			0
$718$	−716.517	−	1241.04i	−0.0372426	−	0.0645061i
$719$	−17588.1			−0.912275			−0.456138	−	0.889909i	$-0.650767\pi$
$719$	−17588.1			−0.912275			−0.456138	+	0.889909i	$0.650767\pi$
$720$		0			0
$721$	−5332.40			−0.275435
$722$	−111.861	−	193.748i	−0.00576596	−	0.00998693i
$723$		0			0
$724$	10069.8	−	17441.4i	0.516907	−	0.895309i
$725$	46.7964	−	81.0537i	0.00239721	−	0.00415208i
$726$		0			0
$727$	−2802.69	−	4854.40i	−0.142979	−	0.247648i	0.785638	−	0.618687i	$-0.212335\pi$
$727$	−2802.69	−	4854.40i	−0.142979	−	0.247648i	−0.928617	+	0.371039i	$0.879002\pi$
$728$	−635.491			−0.0323528
$729$		0			0
$730$	−532.600			−0.0270033
$731$	11695.8	+	20257.7i	0.591771	+	1.02498i
$732$		0			0
$733$	−7460.04	+	12921.2i	−0.375911	+	0.651097i	−0.990463	−	0.137779i	$-0.956004\pi$
$733$	−7460.04	+	12921.2i	−0.375911	+	0.651097i	0.614552	+	0.788877i	$0.289337\pi$
$734$	786.963	−	1363.06i	0.0395740	−	0.0685443i
$735$		0			0
$736$	3246.60	+	5623.27i	0.162597	+	0.281626i
$737$	−17127.6			−0.856042
$738$		0			0
$739$	−27418.8			−1.36484			−0.682421	−	0.730959i	$-0.739073\pi$
$739$	−27418.8			−1.36484			−0.682421	+	0.730959i	$0.739073\pi$
$740$	1239.82	+	2147.44i	0.0615903	+	0.106677i
$741$		0			0
$742$	−104.926	+	181.737i	−0.00519131	+	0.00899161i
$743$	−12272.1	+	21255.9i	−0.605948	+	1.04953i	0.385953	+	0.922518i	$0.373873\pi$
$743$	−12272.1	+	21255.9i	−0.605948	+	1.04953i	−0.991901	+	0.127014i	$0.959461\pi$
$744$		0			0
$745$	357.777	+	619.687i	0.0175945	+	0.0304746i
$746$	−162.712			−0.00798569
$747$		0			0
$748$	−11131.5			−0.544128
$749$	−6605.92	−	11441.8i	−0.322263	−	0.558176i
$750$		0			0
$751$	−767.283	+	1328.97i	−0.0372817	+	0.0645738i	−0.884064	−	0.467365i	$-0.845203\pi$
$751$	−767.283	+	1328.97i	−0.0372817	+	0.0645738i	0.846782	+	0.531939i	$0.178537\pi$
$752$	4926.13	−	8532.30i	0.238880	−	0.413752i
$753$		0			0
$754$	8.80102	+	15.2438i	0.000425085	+	0.000736269i
$755$	−1084.21			−0.0522627
$756$		0			0
$757$	−18051.1			−0.866681			−0.433341	−	0.901230i	$-0.642665\pi$
$757$	−18051.1			−0.866681			−0.433341	+	0.901230i	$0.642665\pi$
$758$	−301.823	−	522.773i	−0.0144627	−	0.0250501i
$759$		0			0
$760$	630.194	−	1091.53i	0.0300783	−	0.0520972i
$761$	6462.29	−	11193.0i	0.307829	−	0.533176i	−0.670058	−	0.742309i	$-0.733731\pi$
$761$	6462.29	−	11193.0i	0.307829	−	0.533176i	0.977887	+	0.209133i	$0.0670642\pi$
$762$		0			0
$763$	3961.61	+	6861.71i	0.187968	+	0.325571i
$764$	19037.8			0.901522
$765$		0			0
$766$	935.491			0.0441262
$767$	−6634.70	−	11491.6i	−0.312341	−	0.540990i
$768$		0			0
$769$	1686.16	−	2920.51i	0.0790695	−	0.136952i	−0.823779	−	0.566911i	$-0.808138\pi$
$769$	1686.16	−	2920.51i	0.0790695	−	0.136952i	0.902849	+	0.429958i	$0.141472\pi$
$770$	116.661	−	202.063i	0.00545996	−	0.00945692i
$771$		0			0
$772$	14137.6	+	24487.0i	0.659097	+	1.14159i
$773$	27152.6			1.26341			0.631703	−	0.775211i	$-0.282356\pi$
$773$	27152.6			1.26341			0.631703	+	0.775211i	$0.282356\pi$
$774$		0			0
$775$	−6291.59			−0.291614
$776$	−464.901	−	805.232i	−0.0215064	−	0.0372502i
$777$		0			0
$778$	675.742	−	1170.42i	0.0311395	−	0.0539352i
$779$	9216.83	−	15964.0i	0.423912	−	0.734236i
$780$		0			0
$781$	−14623.1	−	25327.9i	−0.669982	−	1.16044i
$782$	−1506.89			−0.0689083
$783$		0			0
$784$	−17168.2			−0.782080
$785$	3371.08	+	5838.88i	0.153272	+	0.265476i
$786$		0			0
$787$	12606.0	−	21834.3i	0.570974	−	0.988957i	−0.425492	−	0.904962i	$-0.639899\pi$
$787$	12606.0	−	21834.3i	0.570974	−	0.988957i	0.996466	−	0.0839943i	$-0.0267677\pi$
$788$	4938.08	−	8553.01i	0.223238	−	0.386660i
$789$		0			0
$790$	268.969	+	465.868i	0.0121133	+	0.0209808i
$791$	−11468.2			−0.515500
$792$		0			0
$793$	−20407.0			−0.913838
$794$	−623.386	−	1079.74i	−0.0278629	−	0.0482599i
$795$		0			0
$796$	2058.72	−	3565.80i	0.0916700	−	0.158777i
$797$	19588.5	−	33928.2i	0.870588	−	1.50790i	0.00919851	−	0.999958i	$-0.497072\pi$
$797$	19588.5	−	33928.2i	0.870588	−	1.50790i	0.861390	−	0.507945i	$-0.169595\pi$
$798$		0			0
$799$	3451.75	+	5978.61i	0.152834	+	0.264716i
$800$	835.644			0.0369306
$801$		0			0
$802$	313.764			0.0138147
$803$	−9590.16	−	16610.6i	−0.421456	−	0.729983i
$804$		0			0
$805$	−4110.35	+	7119.33i	−0.179964	+	0.311706i
$806$	591.631	−	1024.74i	0.0258552	−	0.0447826i
$807$		0			0
$808$	691.593	+	1197.87i	0.0301116	+	0.0521548i
$809$	36739.0			1.59663			0.798316	−	0.602239i	$-0.205725\pi$
$809$	36739.0			1.59663			0.798316	+	0.602239i	$0.205725\pi$
$810$		0			0
$811$	−29660.0			−1.28422			−0.642111	−	0.766611i	$-0.721941\pi$
$811$	−29660.0			−1.28422			−0.642111	+	0.766611i	$0.721941\pi$
$812$	−126.258	−	218.685i	−0.00545662	−	0.00945115i
$813$		0			0
$814$	171.549	−	297.132i	0.00738674	−	0.0127942i
$815$	2599.62	−	4502.68i	0.111731	−	0.193524i
$816$		0			0
$817$	−23799.7	−	41222.2i	−1.01915	−	1.76522i
$818$	549.405			0.0234835
$819$		0			0
$820$	8142.54			0.346768
$821$	10056.6	+	17418.6i	0.427501	+	0.740453i	0.996650	−	0.0817808i	$-0.0260607\pi$
$821$	10056.6	+	17418.6i	0.427501	+	0.740453i	−0.569149	+	0.822234i	$0.692727\pi$
$822$		0			0
$823$	−2687.02	+	4654.06i	−0.113808	+	0.197121i	−0.917303	−	0.398191i	$-0.869638\pi$
$823$	−2687.02	+	4654.06i	−0.113808	+	0.197121i	0.803495	+	0.595312i	$0.202971\pi$
$824$	−880.277	+	1524.68i	−0.0372159	+	0.0644598i
$825$		0			0
$826$	−365.697	−	633.406i	−0.0154046	−	0.0266816i
$827$	−27865.2			−1.17167			−0.585833	−	0.810432i	$-0.699233\pi$
$827$	−27865.2			−1.17167			−0.585833	+	0.810432i	$0.699233\pi$
$828$		0			0
$829$	24363.1			1.02070			0.510352	−	0.859965i	$-0.329515\pi$
$829$	24363.1			1.02070			0.510352	+	0.859965i	$0.329515\pi$
$830$	−470.407	−	814.768i	−0.0196724	−	0.0340735i
$831$		0			0
$832$	6721.15	−	11641.4i	0.280065	−	0.485086i
$833$	6014.91	−	10418.1i	0.250185	−	0.433333i
$834$		0			0
$835$	8317.61	+	14406.5i	0.344722	+	0.597076i
$836$	22651.4			0.937099
$837$		0			0
$838$	−430.007			−0.0177259
$839$	−17765.3	−	30770.4i	−0.731020	−	1.26616i	−0.956448	−	0.291903i	$-0.905711\pi$
$839$	−17765.3	−	30770.4i	−0.731020	−	1.26616i	0.225428	−	0.974260i	$-0.427622\pi$
$840$		0			0
$841$	12187.5	−	21109.4i	0.499713	−	0.865528i
$842$	234.363	−	405.928i	0.00959226	−	0.0166143i
$843$		0			0
$844$	−71.0996	−	123.148i	−0.00289970	−	0.00502243i
$845$	7375.13			0.300251
$846$		0			0
$847$	−2862.68			−0.116131
$848$	−4482.22	−	7763.42i	−0.181509	−	0.314383i
$849$		0			0
$850$	−96.9648	+	167.948i	−0.00391278	+	0.00677714i
$851$	−6044.25	+	10468.9i	−0.243471	+	0.421705i
$852$		0			0
$853$	−17223.8	−	29832.4i	−0.691360	−	1.19747i	−0.971392	−	0.237480i	$-0.923679\pi$
$853$	−17223.8	−	29832.4i	−0.691360	−	1.19747i	0.280032	−	0.959991i	$-0.409655\pi$
$854$	−1124.81			−0.0450705
$855$		0			0
$856$	−4362.05			−0.174173
$857$	10003.4	+	17326.4i	0.398729	+	0.690618i	0.993569	−	0.113225i	$-0.0361182\pi$
$857$	10003.4	+	17326.4i	0.398729	+	0.690618i	−0.594841	+	0.803844i	$0.702785\pi$
$858$		0			0
$859$	−893.190	+	1547.05i	−0.0354776	+	0.0614490i	−0.883219	−	0.468961i	$-0.844629\pi$
$859$	−893.190	+	1547.05i	−0.0354776	+	0.0614490i	0.847741	+	0.530410i	$0.177962\pi$
$860$	10512.8	−	18208.8i	0.416842	−	0.721992i
$861$		0			0
$862$	−828.764	−	1435.46i	−0.0327469	−	0.0567192i
$863$	−12151.9			−0.479322			−0.239661	−	0.970857i	$-0.577036\pi$
$863$	−12151.9			−0.479322			−0.239661	+	0.970857i	$0.577036\pi$
$864$		0			0
$865$	−5971.27			−0.234716
$866$	370.811	+	642.263i	0.0145504	+	0.0252021i
$867$		0			0
$868$	−8487.43	+	14700.7i	−0.331892	+	0.574854i
$869$	−9686.27	+	16777.1i	−0.378118	+	0.654919i
$870$		0			0
$871$	7303.02	+	12649.2i	0.284102	+	0.492080i
$872$	2615.94			0.101591
$873$		0			0
$874$	3066.36			0.118674
$875$	528.982	+	916.224i	0.0204376	+	0.0353989i
$876$		0			0
$877$	9436.64	−	16344.7i	0.363344	−	0.629330i	−0.625165	−	0.780493i	$-0.714968\pi$
$877$	9436.64	−	16344.7i	0.363344	−	0.629330i	0.988509	+	0.151163i	$0.0483017\pi$
$878$	−425.119	+	736.328i	−0.0163406	+	0.0283028i
$879$		0			0
$880$	4983.51	+	8631.69i	0.190902	+	0.330653i
$881$	−23587.2			−0.902014			−0.451007	−	0.892520i	$-0.648935\pi$
$881$	−23587.2			−0.902014			−0.451007	+	0.892520i	$0.648935\pi$
$882$		0			0
$883$	−29504.5			−1.12447			−0.562234	−	0.826978i	$-0.690058\pi$
$883$	−29504.5			−1.12447			−0.562234	+	0.826978i	$0.690058\pi$
$884$	4746.35	+	8220.92i	0.180585	+	0.312782i
$885$		0			0
$886$	204.360	−	353.963i	0.00774901	−	0.0134217i
$887$	1238.02	−	2144.31i	0.0468643	−	0.0811714i	−0.841642	−	0.540036i	$-0.818410\pi$
$887$	1238.02	−	2144.31i	0.0468643	−	0.0811714i	0.888506	+	0.458865i	$0.151744\pi$
$888$		0			0
$889$	5003.60	+	8666.49i	0.188769	+	0.326957i
$890$	1316.89			0.0495981
$891$		0			0
$892$	−7886.13			−0.296017
$893$	−7023.94	−	12165.8i	−0.263211	−	0.455894i
$894$		0			0
$895$	−5809.25	+	10061.9i	−0.216963	+	0.375791i
$896$	1502.09	−	2601.69i	0.0560058	−	0.0970048i
$897$		0			0
$898$	1162.82	+	2014.06i	0.0432112	+	0.0748440i
$899$	942.157			0.0349529
$900$		0			0
$901$	6281.40			0.232257
$902$	−563.326	−	975.709i	−0.0207946	−	0.0360173i
$903$		0			0
$904$	−1893.17	+	3279.07i	−0.0696527	+	0.120642i
$905$	6317.80	−	10942.7i	0.232056	−	0.401933i
$906$		0			0
$907$	13375.5	+	23167.1i	0.489666	+	0.848126i	0.999929	−	0.0118922i	$-0.00378549\pi$
$907$	13375.5	+	23167.1i	0.489666	+	0.848126i	−0.510264	+	0.860018i	$0.670452\pi$
$908$	−27312.1			−0.998221
$909$		0			0
$910$	−198.972			−0.00724819
$911$	6334.11	+	10971.0i	0.230360	+	0.398996i	0.957914	−	0.287055i	$-0.0926762\pi$
$911$	6334.11	+	10971.0i	0.230360	+	0.398996i	−0.727554	+	0.686051i	$0.759343\pi$
$912$		0			0
$913$	16940.6	−	29341.9i	0.614076	−	1.06361i
$914$	−452.739	+	784.167i	−0.0163843	+	0.0283785i
$915$		0			0
$916$	4381.61	+	7589.16i	0.158048	+	0.273748i
$917$	−19075.1			−0.686930
$918$		0			0
$919$	46565.5			1.67144			0.835721	−	0.549155i	$-0.185050\pi$
$919$	46565.5			1.67144			0.835721	+	0.549155i	$0.185050\pi$
$920$	1357.08	+	2350.53i	0.0486322	+	0.0842334i
$921$		0			0
$922$	554.779	−	960.905i	0.0198163	−	0.0343229i
$923$	−12470.3	+	21599.1i	−0.444706	+	0.770253i
$924$		0			0
$925$	777.866	+	1347.30i	0.0276498	+	0.0478909i
$926$	556.940			0.0197648
$927$		0			0
$928$	−125.136			−0.00442651
$929$	2305.46	+	3993.17i	0.0814205	+	0.141024i	0.903860	−	0.427828i	$-0.140721\pi$
$929$	2305.46	+	3993.17i	0.0814205	+	0.141024i	−0.822440	+	0.568852i	$0.807388\pi$
$930$		0			0
$931$	−12239.7	+	21199.8i	−0.430870	+	0.746289i
$932$	−17771.4	+	30780.9i	−0.624593	+	1.08183i
$933$		0			0
$934$	−750.354	−	1299.65i	−0.0262873	−	0.0455309i
$935$	−6983.91			−0.244276
$936$		0			0
$937$	−6625.43			−0.230996			−0.115498	−	0.993308i	$-0.536846\pi$
$937$	−6625.43			−0.230996			−0.115498	+	0.993308i	$0.536846\pi$
$938$	402.534	+	697.209i	0.0140119	+	0.0242694i
$939$		0			0
$940$	3102.63	−	5373.91i	0.107656	−	0.186465i
$941$	−21721.3	+	37622.4i	−0.752491	+	1.30335i	0.194121	+	0.980978i	$0.437815\pi$
$941$	−21721.3	+	37622.4i	−0.752491	+	1.30335i	−0.946612	+	0.322375i	$0.895519\pi$
$942$		0			0
$943$	19847.8	+	34377.4i	0.685402	+	1.18715i
$944$	31243.7			1.07722
$945$		0			0
$946$	−2909.24			−0.0999868
$947$	16461.2	+	28511.7i	0.564855	+	0.978357i	0.997063	+	0.0765835i	$0.0244012\pi$
$947$	16461.2	+	28511.7i	0.564855	+	0.978357i	−0.432208	+	0.901774i	$0.642265\pi$
$948$		0			0
$949$	−8178.28	+	14165.2i	−0.279745	+	0.484533i
$950$	197.313	−	341.756i	0.00673861	−	0.0116716i
$951$		0			0
$952$	524.232	+	907.996i	0.0178471	+	0.0309121i
$953$	−20253.5			−0.688430			−0.344215	−	0.938891i	$-0.611855\pi$
$953$	−20253.5			−0.688430			−0.344215	+	0.938891i	$0.611855\pi$
$954$		0			0
$955$	11944.3			0.404722
$956$	−26077.6	−	45167.8i	−0.882229	−	1.52806i
$957$		0			0
$958$	255.272	−	442.144i	0.00860904	−	0.0149113i
$959$	2004.68	−	3472.20i	0.0675020	−	0.116917i
$960$		0			0
$961$	−16771.8	−	29049.7i	−0.562983	−	0.975116i
$962$	−292.587			−0.00980602
$963$		0			0
$964$	1676.16			0.0560015
$965$	8869.93	+	15363.2i	0.295889	+	0.512496i
$966$		0			0
$967$	−1618.56	+	2803.43i	−0.0538257	+	0.0932289i	−0.891683	−	0.452661i	$-0.850475\pi$
$967$	−1618.56	+	2803.43i	−0.0538257	+	0.0932289i	0.837857	+	0.545890i	$0.183808\pi$
$968$	−472.573	+	818.521i	−0.0156912	+	0.0271780i
$969$		0			0
$970$	−145.560	−	252.118i	−0.00481820	−	0.00834537i
$971$	1731.06			0.0572114			0.0286057	−	0.999591i	$-0.490893\pi$
$971$	1731.06			0.0572114			0.0286057	+	0.999591i	$0.490893\pi$
$972$		0			0
$973$	−1159.86			−0.0382151
$974$	1230.23	+	2130.81i	0.0404712	+	0.0700982i
$975$		0			0
$976$	24024.8	−	41612.1i	0.787924	−	1.36472i
$977$	17273.4	−	29918.5i	0.565636	−	0.979710i	−0.431354	−	0.902183i	$-0.641964\pi$
$977$	17273.4	−	29918.5i	0.565636	−	0.979710i	0.996990	−	0.0775275i	$-0.0247026\pi$
$978$		0			0
$979$	23712.3	+	41071.0i	0.774106	+	1.34079i
$980$	−10813.1			−0.352460
$981$		0			0
$982$	163.201			0.00530343
$983$	10226.6	+	17713.0i	0.331818	+	0.574726i	0.982868	−	0.184309i	$-0.0590046\pi$
$983$	10226.6	+	17713.0i	0.331818	+	0.574726i	−0.651050	+	0.759035i	$0.725671\pi$
$984$		0			0
$985$	3098.16	−	5366.17i	0.100219	−	0.173584i
$986$	14.5203	−	25.1500i	0.000468987	−	0.000812310i
$987$		0			0
$988$	−9658.31	−	16728.7i	−0.311004	−	0.538675i
$989$	102502.			3.29563
$990$		0			0
$991$	−5387.77			−0.172703			−0.0863513	−	0.996265i	$-0.527521\pi$
$991$	−5387.77			−0.172703			−0.0863513	+	0.996265i	$0.527521\pi$
$992$	4206.03	+	7285.05i	0.134618	+	0.233166i
$993$		0			0
$994$	−687.347	+	1190.52i	−0.0219329	+	0.0379889i
$995$	1291.64	−	2237.19i	0.0411536	−	0.0712801i
$996$		0			0
$997$	10922.4	+	18918.2i	0.346958	+	0.600949i	0.985707	−	0.168466i	$-0.0538813\pi$
$997$	10922.4	+	18918.2i	0.346958	+	0.600949i	−0.638750	+	0.769415i	$0.720548\pi$
$998$	−2525.16			−0.0800929
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.4.e.b.91.2		6
3.2	odd	2		45.4.e.b.31.2	yes	6
9.2	odd	6		45.4.e.b.16.2	✓	6
9.4	even	3		405.4.a.j.1.2		3
9.5	odd	6		405.4.a.h.1.2		3
9.7	even	3	inner	135.4.e.b.46.2		6
15.2	even	4		225.4.k.c.49.3		12
15.8	even	4		225.4.k.c.49.4		12
15.14	odd	2		225.4.e.c.76.2		6
45.2	even	12		225.4.k.c.124.4		12
45.4	even	6		2025.4.a.q.1.2		3
45.14	odd	6		2025.4.a.s.1.2		3
45.29	odd	6		225.4.e.c.151.2		6
45.38	even	12		225.4.k.c.124.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.2	✓	6	9.2	odd	6
45.4.e.b.31.2	yes	6	3.2	odd	2
135.4.e.b.46.2		6	9.7	even	3	inner
135.4.e.b.91.2		6	1.1	even	1	trivial
225.4.e.c.76.2		6	15.14	odd	2
225.4.e.c.151.2		6	45.29	odd	6
225.4.k.c.49.3		12	15.2	even	4
225.4.k.c.49.4		12	15.8	even	4
225.4.k.c.124.3		12	45.38	even	12
225.4.k.c.124.4		12	45.2	even	12
405.4.a.h.1.2		3	9.5	odd	6
405.4.a.j.1.2		3	9.4	even	3
2025.4.a.q.1.2		3	45.4	even	6
2025.4.a.s.1.2		3	45.14	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0874923 - 0.151541i) q^{2} +(3.98469 - 6.90169i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-4.23186 - 7.32979i) q^{7} -2.79440 q^{8} +O(q^{10})\)	\(q+(-0.0874923 - 0.151541i) q^{2} +(3.98469 - 6.90169i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-4.23186 - 7.32979i) q^{7} -2.79440 q^{8} -0.874923 q^{10} +(-15.7541 - 27.2870i) q^{11} +(-13.4348 + 23.2697i) q^{13} +(-0.740510 + 1.28260i) q^{14} +(-31.6330 - 54.7900i) q^{16} +44.3307 q^{17} -90.2082 q^{19} +(-19.9235 - 34.5084i) q^{20} +(-2.75673 + 4.77480i) q^{22} +(97.1287 - 168.232i) q^{23} +(-12.5000 - 21.6506i) q^{25} +4.70176 q^{26} -67.4506 q^{28} +(1.87186 + 3.24215i) q^{29} +(125.832 - 217.947i) q^{31} +(-16.7129 + 28.9476i) q^{32} +(-3.87859 - 6.71792i) q^{34} -42.3186 q^{35} -62.2293 q^{37} +(7.89252 + 13.6703i) q^{38} +(-6.98599 + 12.1001i) q^{40} +(-102.173 + 176.969i) q^{41} +(263.831 + 456.968i) q^{43} -251.101 q^{44} -33.9920 q^{46} +(77.8637 + 134.864i) q^{47} +(135.683 - 235.009i) q^{49} +(-2.18731 + 3.78853i) q^{50} +(107.067 + 185.445i) q^{52} +141.694 q^{53} -157.541 q^{55} +(11.8255 + 20.4823i) q^{56} +(0.327546 - 0.567326i) q^{58} +(-246.923 + 427.683i) q^{59} +(379.742 + 657.732i) q^{61} -44.0373 q^{62} -500.280 q^{64} +(67.1739 + 116.349i) q^{65} +(271.795 - 470.763i) q^{67} +(176.644 - 305.956i) q^{68} +(3.70255 + 6.41300i) q^{70} +928.207 q^{71} +608.739 q^{73} +(5.44459 + 9.43030i) q^{74} +(-359.452 + 622.589i) q^{76} +(-133.338 + 230.949i) q^{77} +(-307.420 - 532.467i) q^{79} -316.330 q^{80} +35.7573 q^{82} +(537.655 + 931.246i) q^{83} +(110.827 - 191.957i) q^{85} +(46.1663 - 79.9623i) q^{86} +(44.0233 + 76.2506i) q^{88} -1505.15 q^{89} +227.416 q^{91} +(-774.055 - 1340.70i) q^{92} +(13.6249 - 23.5991i) q^{94} +(-225.521 + 390.613i) q^{95} +(166.369 + 288.160i) q^{97} -47.4848 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8}+O(q^{10}) \) 6 * q - q^2 - 11 * q^4 + 15 * q^5 + 43 * q^7 + 54 * q^8	\( 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8} - 10 q^{10} + 14 q^{11} - 40 q^{13} - 27 q^{14} + 13 q^{16} + 332 q^{17} - 328 q^{19} + 55 q^{20} + 376 q^{22} + 171 q^{23} - 75 q^{25} - 868 q^{26} - 1034 q^{28} - 335 q^{29} + 352 q^{31} - 77 q^{32} + 52 q^{34} + 430 q^{35} + 804 q^{37} - 178 q^{38} + 135 q^{40} + 187 q^{41} + 602 q^{43} - 1964 q^{44} - 402 q^{46} + 665 q^{47} - 430 q^{49} - 25 q^{50} + 456 q^{52} + 1460 q^{53} + 140 q^{55} + 705 q^{56} - 217 q^{58} - 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 3138 q^{64} + 200 q^{65} + 1849 q^{67} - 710 q^{68} + 135 q^{70} - 140 q^{71} - 736 q^{73} - 320 q^{74} - 204 q^{76} - 948 q^{77} + 382 q^{79} + 130 q^{80} - 1150 q^{82} - 831 q^{83} + 830 q^{85} + 1580 q^{86} + 1428 q^{88} - 3438 q^{89} - 1420 q^{91} - 1623 q^{92} + 2077 q^{94} - 820 q^{95} + 282 q^{97} - 4328 q^{98}+O(q^{100}) \) 6 * q - q^2 - 11 * q^4 + 15 * q^5 + 43 * q^7 + 54 * q^8 - 10 * q^10 + 14 * q^11 - 40 * q^13 - 27 * q^14 + 13 * q^16 + 332 * q^17 - 328 * q^19 + 55 * q^20 + 376 * q^22 + 171 * q^23 - 75 * q^25 - 868 * q^26 - 1034 * q^28 - 335 * q^29 + 352 * q^31 - 77 * q^32 + 52 * q^34 + 430 * q^35 + 804 * q^37 - 178 * q^38 + 135 * q^40 + 187 * q^41 + 602 * q^43 - 1964 * q^44 - 402 * q^46 + 665 * q^47 - 430 * q^49 - 25 * q^50 + 456 * q^52 + 1460 * q^53 + 140 * q^55 + 705 * q^56 - 217 * q^58 - 298 * q^59 + 1439 * q^61 + 3228 * q^62 - 3138 * q^64 + 200 * q^65 + 1849 * q^67 - 710 * q^68 + 135 * q^70 - 140 * q^71 - 736 * q^73 - 320 * q^74 - 204 * q^76 - 948 * q^77 + 382 * q^79 + 130 * q^80 - 1150 * q^82 - 831 * q^83 + 830 * q^85 + 1580 * q^86 + 1428 * q^88 - 3438 * q^89 - 1420 * q^91 - 1623 * q^92 + 2077 * q^94 - 820 * q^95 + 282 * q^97 - 4328 * q^98

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